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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:56_2_1_1"/>
not <!--HUMANRECFAILED-->( <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; not <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; not <!--HUMANRECFAILED-->( <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_2_1_1_1"><b>suppose </b></a><a NAME="E1:56_2_1_1_1"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/><div class="add"><a NAME="E2:56_2_1_1_1"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_3.html#K8" target="_self">pr2</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_3.html#K8" target="_self">pr2</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:56_2_1_1_1"/>
 <a href="funct_3.html#K8" target="_self">pr2</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font> is   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span>,<font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_2_1_1_2"><b>suppose </b></a><a NAME="E1:56_2_1_1_2"/>
( <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:56_2_1_1_2"/>
 <a href="funct_3.html#K8" target="_self">pr2</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font> is   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font></span><a href="zfmisc_1.html#K2">:]</a></span>,<font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T113">ZFMISC_1:113</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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